The role of hemoglobin in transporting oxygen in the circulation is clear; that of myoglobin in cardiac and red skeletal muscle is still open to experimentation and modeling. It had been thought to serve as a temporary oxygen store and to facilitate the delivery of oxygen by acting as a diffusive carrier. The idea that myoglobin facilitates the diffusion of 02 in red muscle cells was a natural extrapolation from experiments on facilitated diffusion of 02 across porous membranes containing concentrated solutions of myoglobin or hemoglobin. The experimental evidence for facilitated diffusion in muscle is not as clear and the contribution of theory less obvious, to a great extent because of a lack of concensus on the appropriate models to examine. Yet the problem is of profound importance for biology, not only for our understanding of oxidative metabolism in normal tissue but for our understanding of oxidative metabolism in tumor tissue. For mathematical modeling, it provides an example of a reaction-diffusion problem with nonuniform sinks and difficult boundary conditions. We have examined the role of myoglobin in facilitating oxygen diffusion across a 1-dimensional slab with a saturable consumption chosen to model mitrochondrial consumption at the right boundary. Under these conditions myoglobin does not provide a large increase in oxygen transport for the range of P02primes and diffusion lengths expected for skeletal muscle fibers. The next step will be to look at the pattern of 02 consumption for a slab of 25-50 Mum in thickness with bands of sinks at 5 Mum intervals to simulate the structure of red muscle cells.